GMAT Exam > GMAT Questions > If a and b are two distinct positive integers...
Start Learning for Free
If a and b are two distinct positive integers, what is the remainder when a divides b?
(1) When b is divided by the lowest number that is divisible by both a and b, the result is an integer.
(2) a and b have the same prime factors.
(1) When b is divided by the lowest number that is divisible by both a and b, the result is an integer.
(2) a and b have the same prime factors.
- a)Statement (1) ALONE is sufficient, but statement (2) alone is
not sufficient to answer the question asked - b)Statement (2) ALONE is sufficient, but statement (1) alone is
not sufficient to answer the question asked. - c)BOTH statements (1) and (2) TOGETHER are sufficient to
answer the question asked, but NEITHER statement ALONE
is sufficient to answer the question asked. - d)EACH statement ALONE is sufficient to answer the question
asked. - e)Statements (1) and (2) TOGETHER are NOT sufficient to
answer the question asked, and additional data specific to the
problem are needed.
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If a and b are two distinct positive integers, what is the remainder w...
Step 1 & 2: Understand Question and Draw Inference
- a, b are integers > 0
- a ≠ b
To Find: value of r in b = ax + r, where x and r are positive integers and 0 ≤ r < a
- r = 0, if a divides b completely
- 0 < r < a, if a does not divide b completely
Step 3 : Analyze Statement 1 independent
- When b is divided by the lowest number that is divisible by both a and b, the result is an integer.
- Lowest number that is divisible both a and b = LCM(a, b)
- So, we can write:
where z is a positive integer x……(A) - Now, we know that LCM(a, b) will have a as its factor. So, LCM(a, b) divided by a will result in an integer. So, we can write
where d is a positive integer .....(B) - Using (A) and (B), we can write
- Comparing the above equation with b = ax + r, we see that r = 0
- Thus, the remainder will be 0
Sufficient to answer
Step 4 : Analyze Statement 2 independent
2. a and b have the same prime factors
- You can also think of it as this way: If a smaller number is divided by a larger number the remainder will always be equal to the smaller number. For example, if 6 is divided by 18, the remainder will be equal to to 6
- So, in this case, we cannot comment on the remainder when a divides b
Insufficient to answer.
Step 5: Analyze Both Statements Together (if needed)
As we have a unique answer from step-3, this step is not required.
Answer: A
Answer: A
Most Upvoted Answer
If a and b are two distinct positive integers, what is the remainder w...
Step 1 & 2: Understand Question and Draw Inference
- a, b are integers > 0
- a ≠ b
To Find: value of r in b = ax + r, where x and r are positive integers and 0 ≤ r < a
- r = 0, if a divides b completely
- 0 < r < a, if a does not divide b completely
Step 3 : Analyze Statement 1 independent
- When b is divided by the lowest number that is divisible by both a and b, the result is an integer.
- Lowest number that is divisible both a and b = LCM(a, b)
- So, we can write:
where z is a positive integer x……(A) - Now, we know that LCM(a, b) will have a as its factor. So, LCM(a, b) divided by a will result in an integer. So, we can write
where d is a positive integer .....(B) - Using (A) and (B), we can write
- Comparing the above equation with b = ax + r, we see that r = 0
- Thus, the remainder will be 0
Sufficient to answer
Step 4 : Analyze Statement 2 independent
2. a and b have the same prime factors
- You can also think of it as this way: If a smaller number is divided by a larger number the remainder will always be equal to the smaller number. For example, if 6 is divided by 18, the remainder will be equal to to 6
- So, in this case, we cannot comment on the remainder when a divides b
Insufficient to answer.
Step 5: Analyze Both Statements Together (if needed)
As we have a unique answer from step-3, this step is not required.
Answer: A
Answer: A
Free Test
FREE
| Start Free Test |
Community Answer
If a and b are two distinct positive integers, what is the remainder w...
Statement (1): When b is divided by the lowest number that is divisible by both a and b, the result is an integer.
This statement tells us that the lowest common multiple (LCM) of a and b is divisible by both a and b. In other words, a divides the LCM of a and b. However, this does not give us any information about the remainder when a divides b. Therefore, statement (1) alone is not sufficient to answer the question asked.
Statement (2): a and b have the same prime factors.
This statement tells us that a and b have the same prime factors. For example, if a = 2^3 * 3^2 and b = 2^2 * 3^3, then a and b have the same prime factors (2 and 3). However, this does not give us any information about the remainder when a divides b. Therefore, statement (2) alone is not sufficient to answer the question asked.
Both Statements Together:
When we consider both statements together, we can deduce some information. Since a and b have the same prime factors, we can express them as a = p1^x1 * p2^x2 * ... * pn^xn and b = p1^y1 * p2^y2 * ... * pn^yn, where p1, p2, ..., pn are the prime factors common to both a and b, and x1, x2, ..., xn and y1, y2, ..., yn are the respective exponents.
If we divide b by a, we can express the remainder as (p1^y1 * p2^y2 * ... * pn^yn) % (p1^x1 * p2^x2 * ... * pn^xn). Since a and b have the same prime factors, the prime factorization of b contains all the prime factors of a. Therefore, the remainder will be 0 when a divides b.
Hence, both statements together are sufficient to answer the question asked.
Therefore, the correct answer is option (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
This statement tells us that the lowest common multiple (LCM) of a and b is divisible by both a and b. In other words, a divides the LCM of a and b. However, this does not give us any information about the remainder when a divides b. Therefore, statement (1) alone is not sufficient to answer the question asked.
Statement (2): a and b have the same prime factors.
This statement tells us that a and b have the same prime factors. For example, if a = 2^3 * 3^2 and b = 2^2 * 3^3, then a and b have the same prime factors (2 and 3). However, this does not give us any information about the remainder when a divides b. Therefore, statement (2) alone is not sufficient to answer the question asked.
Both Statements Together:
When we consider both statements together, we can deduce some information. Since a and b have the same prime factors, we can express them as a = p1^x1 * p2^x2 * ... * pn^xn and b = p1^y1 * p2^y2 * ... * pn^yn, where p1, p2, ..., pn are the prime factors common to both a and b, and x1, x2, ..., xn and y1, y2, ..., yn are the respective exponents.
If we divide b by a, we can express the remainder as (p1^y1 * p2^y2 * ... * pn^yn) % (p1^x1 * p2^x2 * ... * pn^xn). Since a and b have the same prime factors, the prime factorization of b contains all the prime factors of a. Therefore, the remainder will be 0 when a divides b.
Hence, both statements together are sufficient to answer the question asked.
Therefore, the correct answer is option (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
Attention GMAT Students!
To make sure you are not studying endlessly, EduRev has designed GMAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in GMAT.
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
If a and b are two distinct positive integers, what is the remainder when a divides b?(1) When b is divided by the lowest number that is divisible by both a and b, the result is an integer.(2) a and b have the same prime factors.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer?
Question Description
If a and b are two distinct positive integers, what is the remainder when a divides b?(1) When b is divided by the lowest number that is divisible by both a and b, the result is an integer.(2) a and b have the same prime factors.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If a and b are two distinct positive integers, what is the remainder when a divides b?(1) When b is divided by the lowest number that is divisible by both a and b, the result is an integer.(2) a and b have the same prime factors.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are two distinct positive integers, what is the remainder when a divides b?(1) When b is divided by the lowest number that is divisible by both a and b, the result is an integer.(2) a and b have the same prime factors.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer?.
If a and b are two distinct positive integers, what is the remainder when a divides b?(1) When b is divided by the lowest number that is divisible by both a and b, the result is an integer.(2) a and b have the same prime factors.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If a and b are two distinct positive integers, what is the remainder when a divides b?(1) When b is divided by the lowest number that is divisible by both a and b, the result is an integer.(2) a and b have the same prime factors.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are two distinct positive integers, what is the remainder when a divides b?(1) When b is divided by the lowest number that is divisible by both a and b, the result is an integer.(2) a and b have the same prime factors.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer?.
Solutions for If a and b are two distinct positive integers, what is the remainder when a divides b?(1) When b is divided by the lowest number that is divisible by both a and b, the result is an integer.(2) a and b have the same prime factors.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of If a and b are two distinct positive integers, what is the remainder when a divides b?(1) When b is divided by the lowest number that is divisible by both a and b, the result is an integer.(2) a and b have the same prime factors.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If a and b are two distinct positive integers, what is the remainder when a divides b?(1) When b is divided by the lowest number that is divisible by both a and b, the result is an integer.(2) a and b have the same prime factors.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If a and b are two distinct positive integers, what is the remainder when a divides b?(1) When b is divided by the lowest number that is divisible by both a and b, the result is an integer.(2) a and b have the same prime factors.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If a and b are two distinct positive integers, what is the remainder when a divides b?(1) When b is divided by the lowest number that is divisible by both a and b, the result is an integer.(2) a and b have the same prime factors.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If a and b are two distinct positive integers, what is the remainder when a divides b?(1) When b is divided by the lowest number that is divisible by both a and b, the result is an integer.(2) a and b have the same prime factors.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup